T(n)^2=T(T(n))+T(T(n)-1)

Theorem

The following formula holds for $n=2,3,4,\ldots$: $$T(n)^2=T(T(n))+T(T(n)-1),$$ where $T(n)$ denotes the $n$th triangular number.

References

• V.E. Hoggatt, Jr and Marjorie Bicknell: Triangular numbers (1974)... (previous)... (next) $(1.4)$